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$I=\int\limits_{0}^{\frac{\Pi }{2}}e^{3x}\times\sin5xdx$Đặt $$\begin{cases}u=\sin 5x \\ dv=e^{3x}dx \end{cases}$$ => $$\begin{cases}du=5\cos 5xdx \\ v=\frac{1}{3}e^{3x} \end{cases}$$ $I=\sin 5x\times\frac{1}{3}e^{3x}\prod_{0}^{\frac{\Pi }{2}} - \int\limits_{0}^{\frac{\Pi }{2}}\frac{5}{3}e^{3x}\times\cos 5xdx$Tính $J=\int\limits_{0}^{\frac{\Pi }{2}}\frac{5}{3}e^{3x}\times\cos 5xdx$Đặt $$\begin{cases}u=\cos5 x \\ dv= e^{3x}dx\end{cases}$$ => $$\begin{cases}du=-5\sin 5xdx \\ v=\frac{1}{3}e^{3x} \end{cases}$$ $J=\frac{5}{9}e^{3x}\times cos 5x\prod_{0}^{\frac{\Pi }{2}} + \frac{25}{9}\int\limits_{0}^{\frac{\Pi }{2}}e^{3x}\times\sin 5xdx$$=\frac{5}{9} + \frac{25}{9} I$$I=\frac{1}{3}e^{\frac{3\Pi }{2}} - \frac{5}{9} - \frac{25}{9} I$$I=\frac{3}{34}e^{\frac{3\Pi }{2}} - \frac{5}{34}$

$I=\int\limits_{0}^{\frac{\Pi }{2}}e^{3x}\times\sin5xdx$Đặt $ $$\begin{cases}u=\sin 5x \\ dv=e^{3x}dx \end{cases}$$ => $$\begin{cases}du=5\cos 5xdx \\ v=\frac{1}{3}e^{3x} \end{cases}$$ $$I=\sin 5x\times\frac{1}{3}e^{3x}\prod_{0}^{\frac{\Pi }{2}} - \int\limits_{0}^{\frac{\Pi }{2}}\frac{5}{3}e^{3x}\times\cos 5xdx$Tính $J=\int\limits_{0}^{\frac{\Pi }{2}}\frac{5}{3}e^{3x}\times\cos 5xdx$Đặt $ $$\begin{cases}u=\cos5 x \\ dv= e^{3x}dx\end{cases}$$ => $$\begin{cases}du=-5\sin 5xdx \\ v=\frac{1}{3}e^{3x} \end{cases}$$ $$J=\frac{5}{9}e^{3x}\times cos 5x\prod_{0}^{\frac{\Pi }{2}} + \frac{25}{9}\int\limits_{0}^{\frac{\Pi }{2}}e^{3x}\times\sin 5xdx$$=\frac{5}{9} + \frac{25}{9} I$$I=\frac{1}{3}e^{\frac{3\Pi }{2}} - \frac{5}{9} - \frac{25}{9} I$$I=\frac{3}{34}e^{\frac{3\Pi }{2}} - \frac{5}{34}$